International Association
for Cryptologic Research

In side-channel analysis of public-key algorithms, we usually classify operations based on the differences in power traces produced by different basic operations (such as modular square or modular multiplication) to recover secret information like private keys. The more accurate the segmentation of power traces, the higher the efficiency of their classification. There exist two commonly used methods: one is equidistant segmentation, which requires a fixed number of basic operations and similar trace lengths for each type of operation, leading to limited application scenarios; the other is peak-based segmentation, which relies on personal experience to configure parameters, resulting in insufficient flexibility and poor universality. In this paper, we propose an automated trace segmentation method based on reinforcement learning applicable to a wide range of common implementation of public-key algorithms. The introduction of reinforcement learning, which doesn’t need labels, into trace processing for side-channel analysis marks its debut in this field. Our method has good universality on the traces with varying segment lengths and differing peak heights. By using prioritized experience replay optimized Deep Q-Network algorithm, we reduce the required number of parameters to one, which is the key length. We also employ various techniques to improve the segmentation effectiveness, such as clustering algorithm and enveloped-based feature enhancement. We validate the effectiveness of the new method in nine scenarios involving hardware and software implementations of different public-key algorithms executed on diverse platforms such as microcontrollers, SAKURA-G, and smart cards. Specifically, one of these implementations is protected by time randomization countermeasures. Experimental results show that a basic version of our method can correctly segment most traces. The enhanced version is capable of reconstructing the sequence of operations during trace segmentation, achieving an accuracy rate of 100% for the majority of the traces. For traces that cannot be entirely restored, we utilize reward values of reinforcement learning to correct errors and achieve fully recovery. We also conducted comparative experiments with supervised seq2seq methods, revealing our approach’s 42% higher accuracy in operation recovery and 96% faster time efficiency. In addition, we applied our method to the post-quantum cryptography Kyber, and successfully recovered an intermediate value crucial for deriving the secret key. Besides, power traces collected from these devices have been uploaded as open databases, which are available for researchers engaged in public-key algorithms to conduct related experiments or verify our method.

Code-based cryptography has received a lot of attention recently because it is considered secure under quantum computing. Among them, the QC-MDPC based scheme is one of the most promising due to its excellent performance. QC-MDPC based schemes are usually subject to a small rate of decryption failure, which can leak information about the secret key. This raises two crucial problems: how to accurately estimate the decryption failure rate and how to use the failure information to recover the secret key. However, the two problems are challenging due to the difficulty of geometrically characterizing the bit-flipping decoder employed in QC-MDPC, such as using decoding radius. In this work, we introduce the gathering property and show it is strongly connected with the decryption failure rate of QC-MDPC. Based on this property, we present two results for QC-MDPC based schemes. The first is a new construction of weak keys obtained by extending the keys that have gathering property via ring isomorphism. For the set of weak keys, we present a rigorous analysis of the probability, as well as experimental simulation of the decryption failure rates. Considering BIKE's parameter set targeting $128$-bit security, our result eventually indicates that the average decryption failure rate is lower bounded by $\pr{DFR}_{\text{avg}} \ge 2^{-116.61}$. The second entails two key recovery attacks against CCA secure QC-MDPC schemes using decryption failures in a multi-target setting. The two attacks consider whether or not it is allowed to reuse ciphertexts respectively. In both cases, we show the decryption failures can be used to identify whether a target's secret key satisfies the gathering property. Then using the gathering property as an extra information, we present a modified information set decoding algorithm that efficiently retrieves the target's secret key. For BIKE's parameter set targeting $128$-bit security, we show a key recovery attack with complexity $2^{116.61}$ can be mounted if ciphertexts reusing is not permitted, and the complexity can be reduced to $2^{98.77}$ when ciphertexts reusing is permitted.

$\mathbb{Z}^n$ is one of the simplest types of lattices, but the computational problems on its rotations, such as $\mathbb{Z}$SVP and $\mathbb{Z}$LIP, have been of great interest in cryptography. Recent advances have been made in building cryptographic primitives based on these problems, as well as in developing new algorithms for solving them. However, the theoretical complexity of $\mathbb{Z}$SVP and $\mathbb{Z}$LIP are still not well understood. In this work, we study the problems on rotations of $\mathbb{Z}^n$ by exploiting the symmetry property. We introduce a randomization framework that can be roughly viewed as `applying random automorphisms’ to the output of an oracle, without accessing the automorphism group. Using this framework, we obtain new reduction results for rotations of $\mathbb{Z}^n$. First, we present a reduction from $\mathbb{Z}$LIP to $\mathbb{Z}$SCVP. Here $\mathbb{Z}$SCVP is the problem of finding the shortest characteristic vectors, which is a special case of CVP where the target vector is a deep hole of the lattice. Moreover, we prove a reduction from $\mathbb{Z}$SVP to $\gamma$-$\mathbb{Z}$SVP for any constant $\gamma = O(1)$ in the same dimension, which implies that $\mathbb{Z}$SVP is as hard as its approximate version for any constant approximation factor. Second, we investigate the problem of finding a nontrivial automorphism for a given lattice, which is called LAP. Specifically, we use the randomization framework to show that $\mathbb{Z}$LAP is as hard as $\mathbb{Z}$LIP. We note that our result can be viewed as a $\mathbb{Z}^n$-analogue of Lenstra and Silverberg's result in [JoC2017], but with a different assumption: they assume the $G$-lattice structure, while we assume the access to an oracle that outputs a nontrivial automorphism.

Designing symmetric ciphers for particular applications becomes a hot topic. At EUROCRYPT 2020, Naito, Sasaki and Sugawara invented the threshold implementation friendly cipher SKINNYe-64-256 to meet the requirement of the authenticated encryption PFB_Plus. Soon, Thomas Peyrin pointed out that SKINNYe-64-256 may lose the security expectation due the new tweakey schedule. Although the security issue of SKINNYe-64-256 is still unclear, Naito et al. decided to introduce SKINNYe-64-256 v2 as a response. In this paper, we give a formal cryptanalysis on the new tweakey schedule of SKINNYe-64-256 and discover unexpected differential cancellations in the tweakey schedule. For example, we find the number of cancellations can be up to 8 within 30 consecutive rounds, which is significantly larger than the expected 3 cancellations. This property is derived by the analysis of the updated functions (LFSRs) of the tweakey via linear algebra. Moreover, we take our new discoveries into rectangle, MITM and impossible differential attacks, and adapt the corresponding automatic tools with new constraints from our discoveries. Finally, we find a 41-round related-tweakey rectangle attack on SKINNYe-64-256 and leave a security margin of 3 rounds only. As STK accepts arbitrary tweakey size, but SKINNY and SKINNYe-64-256 v2 only support up to 4n tweakey size. We introduce a new design of tweakey schedule for SKINNY-64 to further extend the supported tweakey size. We give a formal proof that our new tweakey schedule inherits the security requirement of STK and SKINNY.